If you forgot to add a critical insert in the 'Amidah (one of the special additions to Shemoneh 'Esreh at certain times of the year, eg., HaMelech HaKadosh, Ya'aleh VeYavo, etc.), and you realize at the next service that you definitely forgot to say it earlier (eg., you got the date wrong and someone pointed it out to you, or you forgot the next time also but you heard the Sha"Tz say it), do you need to make up for it (Tashlumin, perhaps because it is as if your earlier prayer did not happen), or is Tashlumin not warranted (perhaps because it was a flawed, but fulfilled, prayer)?

Those weren't exclusive interpretations, just exclusive outcomes (either you do or you don't make Tashlumin). The reasons could be many. These are what I came up with off the top of my head. One possible reason to do Tashlumin and one possible reason not to.
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Seth JOct 17 '12 at 19:13

3 Answers
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If one made a mistake in Shomei Esrei that requires repeating (for
example omitting "Vesen Tal U'matar" or Ya'ale Veyavo) and did
not know that he was required to repeat it until after the time of davening passed - he can make it up by praying Tashlumin. Similarly if he was obligated to repeat Shomei Esrei, and forgot until the time passed - he can pray Tashlumin. (Source - Birkas Habayis Shaar 40 Seif 21, as it is considered an ones [out of his control]). However, if he knew he had to pray again and intentionally did not - he cannot pray Tashlumin.

Essentially, yes you should still pray Tashlumin if you would have had to go back and pray at the time.

However, this is only true if you would make up for your mistake. However, if you forget Yaaleh veYavo at Mincha on the last day of Rosh Chodesh then saying two Maarivs wouldn't solve anything because you don't make up the missed Yaaleh veYavo. You can still pray a second time as a Nedava if you want (assuming it isn't Shabbat or Yom Tov).

However, this is only true if the thing you skipped was not essential to Shmoneh Esrei (ie do we consider your earlier prayer a messed up prayer or a non-prayer?). If it was essential, then it is as if you didn't pray and you have to pray Tashlumin just like regular. Examples of things which are essential include Shabbat and Yom Tov according to one opinion in Tosfot (though we rule it is a doubt and one should pray Tashlumin as a Nedava if possible).

This is full of valuable information, but (uncharacteristically for you) it is rather unclear. Your two paragraphs beginning, "However, this is only true," seem to contradict each other a bit, or at least it's not clear what each pgh is limiting with, "However, this."
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Seth JMar 7 '13 at 13:06